Incentive Design in Competitive Resource Allocation: Exploiting Valuation Asymmetry in Tullock Contests

2026-05-07

AI Summary

This study addresses strategic information design in multi-agent Tullock contests, where a central coordinator cannot directly control agents’ actions but can indirectly influence bidding behavior by strategically shaping their perceived valuations of the prize. Preserving the Tullock contest structure to ensure analytical tractability, the work combines Nash equilibrium analysis with nonlinear optimization to reveal that the optimal reported valuation exhibits a parsimonious structure: the coordination problem for any number of subordinate agents reduces to an optimization over just two variables. This approach fully characterizes the equilibrium properties of multi-agent Tullock contests and yields a closed-form solution for the optimal valuation design in the canonical case of two subordinates facing a single opponent. The framework naturally extends to arbitrary numbers of subordinates, substantially reducing computational complexity.

Abstract

In competitive resource allocation, a central coordinator may seek to gain an advantage not by directly controlling subordinate agents, but by strategically manipulating the information they receive. We study this problem within the framework of multi-player Tullock contests, where the coordinator influences subordinate players by designing their reported valuations of the contested prize, a mechanism that preserves the Tullock structure of the subordinates' objectives and thereby enables tractable equilibrium analysis. We first characterize the Nash equilibrium of the general multi-player Tullock contest, establishing how valuations and per-unit costs jointly determine equilibrium bids and payoffs. We then derive the optimal reported valuations for a coordinator managing two subordinates against a single opponent, and show that the structure of the optimal solution extends to contests with an arbitrary number of subordinates, reducing the coordinator's optimization to a two-variable problem regardless of system size.

Problem

• incentive design
• competitive resource allocation
• Tullock contests
• valuation asymmetry
• information manipulation

Innovation

• Tullock contest
• incentive design
• valuation asymmetry
• Nash equilibrium
• resource allocation